Axions from chiral family symmetry

We investigate the possibility that family symmetry, G_F, is spontaneously broken chiral global symmetry. We classify the interesting cases when family symmetry can result in an automatic Peccei-Quinn symmetry U(1)_PQ and thus provide a solution to the strong CP problem. The result disfavors having two or four families. For more than four families, U(1)_PQ is in general automatic. In the case of three families, a unique Higgs sector allows U(1)_PQ in the simplest case of G_F = [SU(3)]³. Cosmological consideration also puts strong constraint on the number of families. For G_F = [SU(N)]³ cosmology singles out the three-family (N = 3) case as a unique solution if there are three light neutrinos. Possible implication of decoupling theorem as applied to family symmetry breaking is also discussed.     

Chiral symmetry breaking and condensates in the rishon model

The rishon model is studied in the limit g_c → 0, α → 0 when its global flavour symmetry is SU(6) × SU(6) × U(1) analogous to six massless flavour QCD. Recently it was shown that the ad hoc breaking SU(6) × SU(6) → SU(3) × SU(3) allows the anomaly constraint to be satisfied. In this paper this is shown to be but one of several successful patterns of chiral symmetry breaking. The condensates required to perform these breakings are fully discussed. A plausibility argument based on single gauge boson exchange is presented which determines the condensate uniquely to be 〈(v_LV_L)³〉 corresponding to the original breaking above. The same argument applies to QCD, which is argued to differ in its chiral behaviour due to the large intrinsic masses of the quarks. The implications of the above condensate and pattern of chiral symmetry breaking for the rishon model include the prediction of integer charged colour octet fermions, a naive mass formula m_e = 2m_u ? m_d, new insight into the parity-violating condensate 〈(v_Lv_L)²(v_Rv_R)〉 and the prediction of 52 new pseudos whose masses are estimated.     

Vector dominance and radiative meson decays

The vector dominance model is reexamined in a semi-empirical approach. Vector-meson-photon couplings are determined from leptonic decays, and the vector-meson mixing angle and a single vector-vector-pseudoscalar coupling constant for an effective VVP lagrangian, which is constrained by Zweig's rule, is calculated from the V→πλ decay widths. The lagrangian is observed to be the same as that obtained by gauging the U(3)_L × U(3)_R hidden symmetry of the nonlinear pseudoscalar chiral lagrangian. The results are in reasonably good agreement with the data. Discrepancies are isolated and found to be substantially cured by a small symmetry breaking mass factor in the coupling constant.     

Topological features of the nonlinear sigma model with Hopf term using chiral lagrangians

We rewrite the O(3) nonlinear sigma model in 2 + 1 dimensions in terms of SU(2) matrices, thereby solving the constraint. The lagrangian has the symmetry SU(2)_Global×U(1)_Local. Static soliton solutions to this lagrangian have energy 4πN as usual. We then show that the Hopf instantons, in the formalism of principle chiral fields, are just the skymions of QCD in 3 + 1 dimensions.     

Electromagnetic interactions in a chiral effective lagrangian for nuclei

Electromagnetic (EM) interactions are incorporated in a recently proposed effective field theory of the nuclear many-body problem. Earlier work with this effective theory exhibited EM couplings that are correct only to lowest order in both the pion fields and the electric charge. The Lorentz-invariant effective field theory contains nucleons, pions, isoscalar scalar (σ) and vector (ω) fields, and isovector vector (ρ) fields. The theory exhibits a nonlinear realization of SU(2)_L × SU(2)_R chiral symmetry and has three desirable features: it uses the same degrees of freedom to describe the currents and the strong-interaction dynamics, it satisfies the symmetries of the underlying QCD, and its parameters can be calibrated using strong-interaction phenomena, like hadron scattering or the empirical properties of finite nuclei. It has been verified that for normal nuclear systems, the effective lagrangian can be expanded systematically in powers of the meson fields (and their derivatives) and can be truncated reliably after the first few orders. The complete EM lagrangian arising from minimal substitution is derived and shown to possess the residual chiral symmetry of massless, two-flavor QCD with EM interactions. The uniqueness of the minimal EM current is proved, and the properties of the isovector vector and axial-vector currents are discussed, generalizing earlier work. The residual chiral symmetry is maintained in additional (non-minimal) EM couplings expressed as a derivative expansion and in implementing vector meson dominance. The role of chiral anomalies in the EM lagrangian is briefly discussed.     

Towards an asymptotic-safety scenario for chiral Yukawa systems

We search for asymptotic safety in a Yukawa system with a chiral U(N _L)_L? ??U(1)_R symmetry, serving as a toy model for the standard-model Higgs sector. Using the functional RG as a nonperturbative tool, the leading-order derivative expansion exhibits admissible non-Gaußian fixed points for 1≤N _L≤57 which arise from a conformal threshold behavior induced by self-balanced boson-fermion fluctuations. If present in the full theory, the fixed point would solve the triviality problem. Moreover, as one fixed point has only one relevant direction even with a reduced hierarchy problem, the Higgs mass as well as the top mass are a prediction of the theory in terms of the Higgs vacuum expectation value. In our toy model, the fixed point is destabilized at higher order due to massless Goldstone and fermion fluctuations, which are particular to our model and have no analogue in the standard model.     

A U(3) nonet scheme for leptons

Introducing six new heavy leptons, we construct a U(3) scheme for leptons. The leptonic U(3) is exactly parallel to the hadronic U(3). One may also introduce quark-like leptonic triplets. A “natural” value of 60° emerges for the mixing angle with m_w = 53 GeV in a theory of weak and electromagnetic interaction based on this U(3) symmetry. There are no neutral ΔS_l = 0 neutrino currents.     

Instantons and the U(1) problem

If instantons spontaneously break the chiral SU(N) × SU(N) symmetry of a non-abelian gauge theory, they break U(1) symmetry in a manner consistent with the chiral Ward identities of the theory. Excitations of the fermion vacuum play a crucial role in this process. A model calculation of the symmetry breaking effect shows a phenomenological structure which differs from that provided by models with many color degrees of freedom.     

Quarks and reggeons

We propose a new algebra which will hopefully contribute to the joint understanding of electromagnetic and weak structure functions and of Regge couplings. It involves an infinite number of form factors of arbitrary complex spin J (with Re(J?1) > 0) and definite signature. The algebra holds exactly in a quark-gluon model when quantized canonically on equal light fronts. If all form factors have k = 0 and J = 1, the algebra closes and becomes U(6) × U(6), with the connecting subgroups being associated with pure quarks and pure antiquark currents, respectively. This doubling of the group leads to exact exchange degeneracy if baryons and mesons consist of qqq and q$\text{q}$ wave functions only.To some lowest approximation, Regge couplings can be calculated by representing U(6) × U(6) on properly mixed quark wave functions. With the mixing parameters fixed by the chiral subgroup, these couplings are determined up to an overall normalization.As an illustration, the coupling of the trajectories ?, ω; A₂, f; A₁, D; Z, Z_sg; π, η; B, H trajectories are estimated for the meson resonances ?, ω; π, η; A₂, f; A₁, D; B, H; A₀, σ. The trajectories π, η; B, H are not in the algebra initially but can be inferred from an extension of PCAC to the bilocal currents (“PCBC”).     

Chiral anomalies and constraints on the gauge group in higher-dimensional supersymmetric Yang-Mills theories

Chiral anomalies for gauge theories in any even dimension are computed and the results applied to supersymmetric theories in D = 6, 8 and 10. For D = 8 there is an anomalous chiral U(1) invariance, just as in D = 4, except for certain special groups. For D = 6 and D = 10 there is no anomalous chiral U(1) symmetry, but the gauge current is anomalous except for certain “anomaly-free” groups. For D = 6 the group is thereby constrained to be one of {SU(2), SU(3), exceptional}, while for D = 10 it is constrained to be one of {SU(n) n ≤ 5, USp(4), E₈}.     

Instantons: Dynamical mass generation,chiral Ward identities and the topological charge correlation function

When dynamical mass generation resulting from the breakdown of chiral symmetry is taken into account, instanton dynamics treated within the dilute gas approximation may satisfy the constraints on the quark condensates and the topological charge correlation function derived by Crewther from an analysis of the chiral Ward identities assuming the absence of a physical axial U(1) Goldstone boson. From a consideration of the contribution of the η′ to the topological charge correlation function, a relationship is derived in which m_η′²f_η′² is proportional to the vacuum energy density.     

A Wilson-Yukawa Model with undoubled chiral fermions in 2D

We consider the fermion mass spectrum in the strong coupling vortex phase (VXS) of a lattice fermion-scalar model with a global U(1)_L × U(1)_R, in two dimensions, in the context of a recently proposed two-cutoff lattice formulation. The fermion doublers are made massive by a strong Wilson-Yukawa coupling, but in contrast with the standard formulation of these type of models, in which the light fermion spectrum was found to be vector-like, we find massless fermions with chiral quantum numbers at finite lattice spacing. When the global symmetry is gauged, this model is expected to give rise to a lattice chiral gauge theory.     

Thirring model with U(n) symmetry: Scale invariant only for fixed values of a coupling constant

Generalizations of the Thirring model to Fermi fields with U(n) symmetry are treated. When interactions quadratic in the SU(n) currents are introduced, scale invariance (with anomalous dimensions) is maintained only for values of the coupling g_v=0 or $\text{g}{}_{\mathrm{<mtext>v</mtext>}}\text{=}\text{4φ}\text{(n+1)}$.     

Quark-lepton symmetry and B − L as the U(1) generator of the electroweak symmetry group

We seek an interpretation of the U(1) part of the electroweak symmetry group in terms of the quantum number B ? L. We show that the electroweak symmetry group, for which U(1) can be interpreted as a local B ? L symmetry, is the left-right symmetry group SU(2)_L × SU(2)_R × U(1)_L+R. The equating of U_L+R(1) to U_B?L(1) should lead to physical consequences which are not shared by standard gauge theory. B ? L may also help to explain the inversion of quark and lepton mass spectra.     

Kac-Moody symmetries of critical ground states

The symmetries of critical ground states of two-dimensional lattice models are investigated. We show how mapping a critical ground state to a model of a rough interface can be used to identify the chiral symmetry algebra of the conformal field theory that describes its scaling limit. This is demonstrated in the case of the six-vertex model, the three-coloring model on the honeycomb lattice, and the four-coloring model on the square lattice. These models are critical and they are described in the continuum by conformal field theories whose symmetry algebras are the su(2)_k=1, su(3)_k=1, and the su(4)_k=1 Kac-Moody algebra, respectively. Our approach is based on the Frenkel-Kac-Segal vertex operator construction of level-one Kac-Moody algebras.     

Spontaneous breaking of global baryon number symmetry

We study the possibility that theU(1) _B global symmetry associated with baryon number is spontaneously broken. We present realistic examples implemented in the context of a suitably extended standardSU(2) _L×U(1)×SU(3)_c model and of a composite model of quarks and leptons. The globalU(1) _B symmetry in both cases is spontaneously broken at a relatively low mass scale without any conflict with observations. The dominant baryon number nonconserving process in these models obeys the ΔB=2 selection rule.     

QED with vector and axial vector types of interaction and dynamical generation of particle masses

We consider a model of electrodynamics with two types of interaction, the vector \((e\bar \psi (\gamma ^\mu A_\mu )\psi )\) and axial vector \((e_A \bar \psi (\gamma ^\mu \gamma ^5 B_\mu )\psi )\) interactions, i.e., with two types of vector gauge fields, which corresponds to the local nature of the complete massless-fermion symmetry group U(1) ? U _A (1). We present a phenomenological model with spontaneous symmetry breaking through which the fermion and the axial vector field B_μ acquire masses. Based on an approximate solution of the Dyson equation for the fermion mass operator, we demonstrate the phenomenon of dynamical chiral symmetry breaking when the field B_μ has mass. We show the possibility of eliminating the axial anomalies in the model under consideration when introducing other types of fermions (quarks) within the standard-model fermion generations. We consider the polarization operator for the field B_μ and the procedure for removing divergences when calculating it. We demonstrate the emergence of a mass pole in the propagator of the particles that correspond to the field B_03BC when chiral symmetry is broken and consider the problems of regularizing closed fermion loops with axial vector vertices in connection with chiral symmetry breaking.     

Spontaneous CP violation in extended technicolor models with horizontal U(2)L ⊗ U(2)R flavor symmetries (I)

The Eichten, Lane, Preskill mechanism for CP violation in extended technicolor (ETC) models is examined in models with “horizontal” U(2)_L ? U(2)_R flavor symmetries. We identify a class of chiral perturbations which generate spontaneous CP violation when the vacuum alignment is determined by Dashen's theorem, and show that, in general, a discrete symmetry must be invoked to avoid strong CP non-conservation. CP-violating phases appearing in the electroweak and broken ETC interactions may be naturally suppressed by ratios of ETC vector boson masses.     

Spontaneous breakdown of the gauge chiral symmetry and the cabibbo angle

From the general treatment of the spontaneous breakdown of the chiral SU(3)xSU(3) group down to the electromagnetic U(l) gauge group it is conjectured that the bare Cabibbo angle isπ/4. Imposing the self-consistency condition of Cabibbo and Maiani on the weak and electromagnetic corrections to the chiral symmetry breaking Hamiltonianh=ε₀ u ₀+ +ε₃ u ₃+ε₈ u ₈ leads to the determination of the physical Cabibbo angle. The agreement with the experimental value is reached when the parametrization ofh of Brandt and Preparata is used.     

Kl3 from factors and (8, 8) model of chiral symmetry breaking

K_l3 form factors are calculated in the single particle approximation to the spectral functions. The so-called sigma terms and current divergences are calculated in the (8, 8) model of chiral symmetry breaking. Comparison with the experimental results and the (3,3¹) + (3¹, 3) model is made. It is concluded that it is not possible to rule out the (8, 8) model in favor of the (3,3¹) + (3¹) + (3¹, 3) model at present.